Q35 / 60 · JEE Advanced 2011 (Paper 2) · Mathematics
Let $\omega=e^{i \pi / 3}$ and $a, b, c, x, y, z$ be non-zero complex numbers such that $a+b+c=x, a+b \omega+c \omega^2=y, a+b \omega^2+c \omega=z$.
Then, the value of $\frac{|x|^2+|y|^2+|z|^2}{|a|^2+|b|^2+|c|^2}$ is
Correct answer: 3
Solution
Here, $\omega=e^{i 2 \pi / 3}$, then only integer solution exists.
Then, $\frac{\left|x^2\right|+\left|y^2\right|+\left|z^2\right|}{\left|a^2\right|+\left|b^2\right|+\left|c^2\right|}=3$
Hence, the correct answer is 3.